Viewed by an observer, such as a marksman, an object of a certain size B fills a certain angle β, independent of the distance E. The formula for this is sin β=B/E. With two known variables, the relationship between the object size, the distance, and the filled observation angle permits the determination of the third (unknown) variable. This relationship is utilized by the so-called stadiametric distance measurement. The angle measurement can be carried out, among other ways, with the aid of reticles in observation and target optics. For this purpose, markings are placed on the reticle, which permit the observer to read off the angle filled by the object. With a known object size, it is possible to calculate the distance with the aid of the angle read off. The attainable accuracy of the results thereby depends on how accurately the angle can be read off and how accurately the size of the pertinent object is known. For simplification, a mathematical linear approximation is thereby carried out.
Although nowadays efficient laser-distance gauges are mostly available, the distance measurement through a reticle continues to play an important role. It is used as an alternative method if the laser-distance gauge fails or when only a passive system can be used because of the risk of a detection of the laser. Therefore, estimating the distance through a reticle is taught, as before, in the training of snipers and also in corresponding sport competitions, the determination of the target distance merely with the aid of the so-called anticipation is promoted. Current target optics, therefore, often continue to contain special markings for the stadiametric distance measurement, without there having been any substantial further development in comparison to methods known for decades.
From the state of the art, target optics are known that utilize the various systems for the distance measurement. The system that is most widespread today is the so-called “mil dot” range finding of a target optics that is provided with points that indicate an angle of one milliradian (mrad). A mrad is defined as the arc length that is 1/1000 of the radian length. A mrad corresponds thereby to 10 cm per 100 m or 1 m per 1000 m, and so forth. This would correspond to an approximate conversion of the approximation (for small angles) into the metric system. Increasingly widespread are reticles that do not use points (used earlier in wire range finding for reasons having to do with manufacturing feasibility), but rather scale lines that also permit finer divisions.
The mrad scale is universally applicable and not linked to a specific object size. It can be used both for distance determination as well as a hitting accuracy correction.
The linearly approximated formulation for the distance determination is as follows:Object size B [m]×1000/Measurement value [mrad]=Distance E [m]
Advantages of the mrad scale are the universal applicability and the possible fine division, which makes a high accuracy possible. A scale with a division of 0.1 mrad is practical with a corresponding enlargement of the optics.
The scale division can also take place in any other angular scale. In the English-speaking realm, minutes of angle (MOA) continue to be widespread; the SI unit (milli)radian, however, is more advantageous in connection with the decimal system, since the ratio 1/1000 brings about a decimal point displacement without an additional factor in calculations.
Such a system can be seen with regard to the “mil dot” range finding, for example, in U.S. Pat. No. 7,185,455 B2. This shows crosshairs with a primary horizontal line of sight and a vertical line of sight that intersect in a target point. Other target marks, in the form of lines, are located on the lines of sight; they form a scale and cut the lines of sight vertically. The distances of the individual target marks on the lines of sight subdivide the scale thereby into specific mrad measurements, for example, of 2.5 mrad (mils). The length of the pertinent target marking also has an mrad division, for example, of 0.1, 0.3, or 0.5. The formula mentioned above is to be used for the calculation of the distance to a target.
The disadvantage hereby is the division with perhaps uneven values needed during the calculation, which mostly cannot be carried out in one's head. For the calculation of the distance, the user is therefore compelled to use a pocket calculator, tabulated values, or a slide rule specially made for this purpose (U.S. Pat. No. 5,960,576). All of these calculation methods lead to the marksman losing sight of the target image during the calculation. Moreover, they require aids which may perhaps not function or may get lost.
The second possibility of the distance determination with the aid of the reticle is a scale adapted to a specific object size. Markings are thereby placed on the reticle, between which a target object of a specific size is adjusted. The marking suitable for the object size is labelled with the corresponding distance. If a suitable target object is present, then the distance can be read off directly and without further calculation.
Target optics known from the military area frequently use markings that correspond to the size of a standing man target (1.5-1.8 m); otherwise, the standard measure of 1 m height is common. Markings that correspond to the shoulder width of a man target (0.45 m or 0.5 m), or alternatively combinations of 1 m height and 0.5 m width, are also widely used. However, the most varied reticles also exist, which are adapted to the size of certain animals or, for example, to vehicle silhouettes (for example, with optics for anti-tank hand guns), which are provided with distance marks. The target optics of battle tanks also often have corresponding reticles as a substitute for a laser-distance gauge that has perhaps failed.
It is problematical hereby that the markings are designed for a specific size of the target object. If an object of the suitable size is not visible, for example, because the target is partially covered, then the markings cannot be used. Furthermore, intermediate values must be estimated with intermediate distances, which is frequently complicated by the separate arrangements of the markings for different distances.